## Course Detail

 Course Name Transforms and Partial Differential Equations Course Code 15 MAT 204 Program B. Tech. in Civil Engineering, B. Tech. (Bachelor of Technology) in Aerospace Engineering, B. Tech. in Chemical Engineering, B. Tech. (Bachelor of Technology) in Mechanical Engineering Semester Three Year Taught 2019

### Syllabus

##### Unit 1

Laplace Transform: Laplace Transforms, Inverse Transforms, Linearity, Shifting, Transforms of Derivatives and Integrals, Differential Equations, Unit Step Function, Second Shifting Theorem, Dirac’s Delta Function. Differentiation and Integration of Transforms.

##### Unit 2

Convolution, Integral Equations, Partial Fractions, Differential Equations, Systems of Differential Equations. (Sections: 6.1 to 6.7)

Fourier Series: Fourier series, Half range Expansions, Parseval’s Identity, Fourier Integrals, Fourier integral theorem. Sine and Cosine Integrals. (Sections:11.1 -11.3)

##### Unit 3

Fourier Transforms: Sine and Cosine Transforms, Properties, Convolution theorem. (Sections: 11.1 -11.3, 11.7-11.9)

Partial Differential Equations: Basic Concepts, Modeling; Vibrating String, Wave Equation, Separation of Variables, Use of Fourier Series, Heat Equation; Solution by Fourier Series. (Sections: 12.1-12.5)

### Text Books

1. Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Ninth Edition, 2012.

### Resources

• Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.
• Larry C. Andrews and Bhimson. K. Shivamoggi, The Integral Transforms for Engineers, Spie Press, Washington, 1999.
• J. L. Schiff, The Laplace Transform, Springer, 1999.

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